Finite Group Databasebeta

← #11884435

Subgroups — #11884435

Order 1152.

1080 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#916C211yesmaximal, characteristic, complemented
2C2×C3×#914C211yesmaximal, characteristic, complemented
3#10595412C211yesmaximal, characteristic, complemented
4#10595244C211yesmaximal, characteristic, complemented
5#10592863C211yesmaximal, characteristic, complemented
6#10591612C211yesmaximal, characteristic, complemented
7#10591597C211yesmaximal, characteristic, complemented
8#10591586C211yesmaximal, characteristic, complemented
9#10591486C211yesmaximal, characteristic, complemented
10#10591450C211yesmaximal, characteristic, complemented
11#10591447C211yesmaximal, characteristic, complemented
12#10590887C211yesmaximal, characteristic, complemented
13#10590833C211yesmaximal, characteristic, complemented
14#10590831C211yesmaximal, characteristic, complemented
15#10590722C211yesmaximal, characteristic, complemented
16#83955—31nomaximal
17#83922—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic, complemented
20C2×C3×#237C2211yescharacteristic
21C2×C3×D3×D4C2211yescharacteristic
22C2×C32×SD16C2211yescharacteristic
23Q8×C3⋊Dic3C2211yescharacteristic, complemented
24D4×C3⋊Dic3C2211yescharacteristic
25C2×C3×#216C2211yescharacteristic, complemented
26C2×C3×#215C2211yescharacteristic
27C2×C3×#213C2211yescharacteristic
28C2×C3×#213C2211yescharacteristic
29C3×#916—24no—
30C3×#914—24no—
31C2×C3×D24C2211yescharacteristic
32C2×C3×#204C2211yescharacteristic, complemented
33C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
34C2×C3×D3×C8C2211yescharacteristic, complemented
35#63980—21no—
36#63976—21no—
37#63961—21no—
38C2×(C2×D3)⋊Dic3—21no—
39#63914—21no—
40#63914C2211yescharacteristic, complemented
41#63908—21no—
42#63908—21no—
43#63908C2211yescharacteristic
44#63908C2211yescharacteristic
45#63908C2211yescharacteristic, complemented
46C4×#625—21no—
47C4×#625C2211yescharacteristic
48#63863C2211yescharacteristic
49#63856C2211yescharacteristic
50C2×#3715C2211yescharacteristic, complemented
51C2×#3713C2211yescharacteristic
52#63662C2211yescharacteristic, complemented
53#63659C2211yescharacteristic
54#63645C2211yescharacteristic, complemented
55#63642C2211yescharacteristic, complemented
56#63572C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63563C2211yescharacteristic
59#63563C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
63C2×C3×AGL(1,ℤ/8)—31no—
64C2×C3×#135—31no—
65#5834—31no—
66#5834—31no—
67#5829—31no—
68#5806—31no—
69C2×#916D311yescharacteristic, complemented
70C2×#914D311yescharacteristic, complemented
71#5239—31no—
72#5238—31no—
73#5238—31no—
74#5217—31no—
75#5187—31no—
76#5185—31no—
77#5176—31no—
78#5174—31no—
79#5172—31no—
80#5166—31no—
81#5164—31no—
82#5164—31no—
83#5164—61no—
84#5158—31no—
85#5157—31no—
86#5156—31no—
87#5154—31no—
88#5150—31no—
89#5150—31no—
90#5134—31no—
91#5127—31no—
92#5115—31no—
93#5111—31no—
94C23×C3×D3—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×D4C2311yescharacteristic
97C22×C3⋊Dic3—21no—
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C22×C3×Dic3—21no—
101C3×#239—22no—
102C3×#239—22no—
103C3×#239—41no—
104C3×#239—41no—
105C3×#237—22no—
106C3×#237—41no—
107C3×D3×D4—22no—
108C3×D3×D4—41no—
109C2×C3×D12—21no—
110C2×C3×D12—21no—
111C2×C3×D12C2311yescharacteristic
112C2×C3×D12C2311yescharacteristic
113C2×C3×D12C2311yescharacteristic
114C2×C3×C4×D3—21no—
115C2×C3×C4×D3—21no—
116C2×C3×C4×D3C2311yescharacteristic
117C2×C3×C4×D3C2311yescharacteristic
118C2×C3×Dic6C2311yescharacteristic
119C2×#625—21no—
120C2×#625—21no—
121C2×#625—21no—
122C2×#625—21no—
123C2×#625—21no—
124C2×#625D411yescharacteristic
125C32×SD16D414yescomplemented
126C2×C32×C8C2311yescharacteristic
127#3757—21no—
128C4⋊(C3⋊Dic3)—21no—
129C4⋊(C3⋊Dic3)C2311yescharacteristic
130C4⋊(C3⋊Dic3)C2311yescharacteristic
131C4×C3⋊Dic3—21no—
132C4×C3⋊Dic3C2311yescharacteristic
133C2×C3⋊(C3⋊C8)C2311yescharacteristic
134C3×#216—22no—
135C3×#215—22no—
136C3×#213—22no—
137C3×#213—22no—
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C3×D24—22no—
141C3×#204—22no—
142C3×ΓL(1,𝔽25)—22no—
143C3×D3×C8—22no—
144#3724—21no—
145#3724D411yescharacteristic
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3—21no—
152(C2×D3)⋊Dic3D411yescharacteristic
153(C2×D3)⋊Dic3D411yescharacteristic
154#3715—41no—
155#3713—41no—
156#3268—91noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C2×C3×#41—31no—
160C22×C3×D4—31no—
161C2×#239C2×D311yescharacteristic
162C2×#239C2×D311yescharacteristic, complemented
163C2×#237C2×D311yescharacteristic
164C2×D3×D4C2×D311yescharacteristic
165C3×AGL(1,ℤ/8)—64no—
166C3×#135—64no—
167C2×C3×Q16—31no—
168C2×C3×SD16—21no—
169C2×C3×SD16—31no—
170C2×C3×SD16—31no—
171C2×C3×SD16C2×D311yescharacteristic
172C2×C3×SD16C2×D311yescharacteristic
173C2×C3×D8—31no—
174C2×C3×D8—31no—
175C2×C3×D8—31no—
176C2×C3×M16—31no—
177C22×C3×C8—31no—
178#953—61no—
179C2×#217—61no—
180#947—31no—
181#946—31no—
182Q8×Dic3—31no—
183Q8×Dic3—31no—
184Q8×Dic3—61no—
185C2×#216C2×D311yescharacteristic, complemented
186C2×#215—31no—
187C2×#215C2×D311yescharacteristic
188#940—31no—
189#940—31no—
190#940—61no—
191#940—61no—
192#939—61no—
193#939—61no—
194#938—31no—
195#938—31no—
196#938—31no—
197#938—61no—
198#938—61no—
199#937—61no—
200#936—31no—
201#935—61no—
202D4×Dic3—31no—
203D4×Dic3—31no—
204D4×Dic3—61no—
205C2×#214—31no—
206C2×#213—31no—
207C2×#213—31no—
208C2×#213C2×D311yescharacteristic
209C2×#213C2×D311yescharacteristic
210#930—31no—
211#930—31no—
212#930—31no—
213#930—61no—
214#930—61no—
215#929—61no—
216C4×#67—31no—
217C4×#67—31no—
218C4×#67—61no—
219C4×#67—61no—
220C2×(C2×D3)⋊C4—61no—
221#924—31no—
222#916—24no—
223#914—24no—
224C2×D24C2×D311yescharacteristic
225C2×#204C2×D311yescharacteristic, complemented
226C2×ΓL(1,𝔽25)C2×D311yescharacteristic
227C2×D3×C8C2×D311yescharacteristic, complemented
228#835—31no—
229#835—31no—
230#835—31no—
231#835—61no—
232#832—31no—
233#832—31no—
234#832—31no—
235#832—31no—
236#832—31no—
237#832—61no—
238#830—31no—
239#830—31no—
240#821—31no—
241#821—31no—
242#821—31no—
243(C2×D3)⋊C8—31no—
244(C2×D3)⋊C8—31no—
245#818—31no—
246#818—31no—
247#818—61no—
248#816—31no—
249#815—31no—
250#815—31no—
251#815—61no—
252Dic3⋊C8—31no—
253Dic3⋊C8—31no—
254C23×C32—21no—
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—42no—
259C22×C3×D3—42no—
260C22×C3×D3—81no—
261C22×C3×D3C2×D411yescharacteristic
262C22×C3×D3C2×D411yescharacteristic
263C32×Q8—21no—
264C32×Q8C2×D412yes—
265C32×D4—21no—
266C32×D4C2×D412yes—
267C2×C32×C4—21no—
268C2×C32×C4C2411yescharacteristic
269C2×C3⋊Dic3—21no—
270C2×C3⋊Dic3—21no—
271C2×C3⋊Dic3—81no—
272C2×C3⋊Dic3C2×D411yescharacteristic
273C2×C3⋊Dic3C2×D411yescharacteristic
274C3×#67—42no—
275C3×#67—42no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—42no—
278C2×C3×Dic3C2×D411yescharacteristic
279C2×C3×Dic3C2×D411yescharacteristic
280C3×D12—21no—
281C3×D12—21no—
282C3×D12—21no—
283C3×D12—21no—
284C3×D12—21no—
285C3×D12—21no—
286C3×D12—42no—
287C3×D12—42no—
288C3×C4×D3—21no—
289C3×C4×D3—21no—
290C3×C4×D3—21no—
291C3×C4×D3—21no—
292C3×C4×D3—42no—
293C3×C4×D3—42no—
294C3×Dic6—21no—
295C3×Dic6—21no—
296#625—41no—
297#625—42no—
298#625—81no—
299#625—81no—
300#625—81no—
301#625—81no—
302C32×C8C2×D412yes—
303C3⋊(C3⋊C8)—21no—
304C3×C3⋊C8—21no—
305C3×C3⋊C8—21no—
306C2×AGL(1,ℤ/8)—31no—
307C2×#135—31no—
308#550—91no—
309#546—91no—
310#496—91no—
311#468—91no—
312#466—91no—
313#464—91no—
314#459—91no—
315#452—91no—
316#449—91no—
317#449—91no—
318#447—91no—
319#440—91no—
320#435—91no—
321C24×C3—61no—
322C23×D3—21no—
323C3×#41—62no—
324C3×#41—62no—
325C3×#41—62no—
326C3×#41—121no—
327C3×#41—121no—
328C3×#41—121no—
329C2×C3×Q8—21no—
330C2×C3×Q8—31no—
331C2×C3×Q8C22×D311yescharacteristic
332C2×C3×Q8C22×D311yescharacteristic
333C2×C3×D4—21no—
334C2×C3×D4—31no—
335C2×C3×D4—31no—
336C2×C3×D4—31no—
337C2×C3×D4—61no—
338C2×C3×D4—61no—
339C2×C3×D4—61no—
340C2×C3×D4—62no—
341C2×C3×D4—61no—
342C2×C3×D4—121no—
343C2×C3×D4C22×D311yescharacteristic
344C2×C3×D4C22×D311yescharacteristic
345C22×C3×C4—31no—
346C22×C3×C4—31no—
347C22×C3×C4—61no—
348C22×C3×C4—61no—
349C22×C3×C4—61no—
350C2×#67—21no—
351C2×#67—21no—
352C2×#67—31no—
353C2×#67—31no—
354C2×#67—61no—
355C2×#67—61no—
356C2×#67—61no—
357C2×#67—61no—
358C2×#67—61no—
359C2×#67—61no—
360C2×#67—61no—
361C2×#67—61no—
362C2×#67—61no—
363C2×#67—61no—
364C22×Dic3—21no—
365C22×Dic3—61no—
366C22×Dic3—61no—
367C22×Dic3—121no—
368#239—22no—
369#239—22no—
370#239—41no—
371#239—41no—
372#237—22no—
373#237—41no—
374D3×D4—22no—
375D3×D4—41no—
376C2×D12—21no—
377C2×D12—21no—
378C2×D12C22×D311yescharacteristic
379C2×D12C22×D311yescharacteristic
380C2×D12C22×D311yescharacteristic
381C2×C4×D3—21no—
382C2×C4×D3—21no—
383C2×C4×D3C22×D311yescharacteristic
384C2×C4×D3C22×D311yescharacteristic
385C2×Dic6C22×D311yescharacteristic
386C3×Q16—62no—
387C3×SD16—24no—
388C3×SD16—62no—
389C3×SD16—62no—
390C3×SD16#6714yescomplemented
391C3×SD16#6714yescomplemented
392C3×D8—62no—
393C3×D8—62no—
394C3×D8—62no—
395C3×M16—62no—
396C2×C3×C8—21no—
397C2×C3×C8—31no—
398C2×C3×C8—31no—
399C2×C3×C8—62no—
400C2×C3×C8C22×D311yescharacteristic
401C2×C3×C8C22×D311yescharacteristic
402#217—31no—
403#217—31no—
404#217—61no—
405#217—61no—
406#217—61no—
407#217—61no—
408#217—61no—
409#217—61no—
410#217—61no—
411#217—61no—
412#217—121no—
413#216—22no—
414#215—22no—
415#215—121no—
416#214—121no—
417#213—22no—
418#213—22no—
419#213—121no—
420#213—121no—
421(C2×D3)⋊C4—31no—
422(C2×D3)⋊C4—31no—
423(C2×D3)⋊C4—61no—
424(C2×D3)⋊C4—61no—
425(C2×D3)⋊C4—61no—
426(C2×D3)⋊C4—61no—
427(C2×D3)⋊C4—61no—
428(C2×D3)⋊C4—61no—
429C4⋊Dic3—31no—
430C4⋊Dic3—31no—
431C4⋊Dic3—31no—
432C4⋊Dic3—31no—
433C4⋊Dic3—61no—
434C4⋊Dic3—61no—
435C4⋊Dic3—61no—
436C4⋊Dic3—61no—
437C4⋊Dic3—121no—
438Dic3⋊C4—31no—
439Dic3⋊C4—31no—
440Dic3⋊C4—61no—
441Dic3⋊C4—61no—
442C4×Dic3—31no—
443C4×Dic3—31no—
444C4×Dic3—61no—
445C4×Dic3—61no—
446C4×Dic3—61no—
447C4×Dic3—121no—
448C2×C3⋊C8—31no—
449C2×C3⋊C8—31no—
450C2×C3⋊C8—61no—
451C2×C3⋊C8C22×D311yescharacteristic
452C2×C3⋊C8C22×D311yescharacteristic
453D24—22no—
454#204—22no—
455ΓL(1,𝔽25)—22no—
456D3×C8—22no—
457C22×C32—22no—
458C22×C32—41no—
459C22×C32—41no—
460C22×C32C22×D411yescharacteristic
461C2×C3×D3—21no—
462C2×C3×D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3—21no—
465C2×C3×D3—21no—
466C2×C3×D3—21no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—84no—
477C32×C4—22no—
478C32×C4C22×D411yescharacteristic
479C32×C4H(5,𝔽2)11yescharacteristic
480C3⋊Dic3—21no—
481C3⋊Dic3—21no—
482C3⋊Dic3—41no—
483C3⋊Dic3—41no—
484C3×Dic3—21no—
485C3×Dic3—21no—
486C3×Dic3—41no—
487C2×#41—31no—
488C2×#41—31no—
489C2×#41—31no—
490C22×D4—31no—
491AGL(1,ℤ/8)—64no—
492#135—64no—
493C2×Q16—31no—
494C2×SD16—31no—
495C2×SD16—31no—
496C2×SD16—91no—
497C2×SD16D3211yescharacteristic
498C2×D8—31no—
499C2×D8—31no—
500C2×D8—31no—
501C2×D8—91no—
502C2×M16—31no—
503C22×C8—31no—
504#127—91no—
505#127—181no—
506#124—91no—
507#123—181no—
508C22⋊Q8—91no—
509#121—91no—
510#121—91no—
511#121—91no—
512#121—181no—
513#121—181no—
514#121—181no—
515#120—181no—
516C4×Q8—91no—
517C4×D4—91no—
518C4×D4—91no—
519C4×D4—181no—
520C2×C22⋊C4—181no—
521#107—91no—
522C4⋊C8—91no—
523#103—91no—
524#103—91no—
525#102—91no—
526#102—91no—
527#102—91no—
528#102—91no—
529C22⋊C8—91no—
530C22⋊C8—91no—
531#97—91no—
532C23×C3—21no—
533C23×C3—21no—
534C23×C3—31no—
535C23×C3—31no—
536C23×C3—41no—
537C23×C3—61no—
538C23×C3—61no—
539C23×C3—61no—
540C23×C3—122no—
541C23×C3—122no—
542C23×C3—241no—
543C22×D3—21no—
544C22×D3—21no—
545C22×D3—21no—
546C22×D3—42no—
547C22×D3—42no—
548C22×D3—81no—
549C22×D3D3×D411yescharacteristic
550C22×D3D3×D411yescharacteristic
551C3×Q8—21no—
552C3×Q8—21no—
553C3×Q8—22no—
554C3×Q8—41no—
555C3×Q8—61no—
556C3×Q8—61no—
557C3×Q8C2×#6712yes—
558C3×Q8C2×#6712yes—
559C3×D4—21no—
560C3×D4—21no—
561C3×D4—22no—
562C3×D4—41no—
563C3×D4—61no—
564C3×D4—61no—
565C3×D4—61no—
566C3×D4—61no—
567C3×D4—61no—
568C3×D4—61no—
569C3×D4—122no—
570C3×D4—122no—
571C3×D4—122no—
572C3×D4—122no—
573C3×D4C2×#6712yes—
574C3×D4C2×#6712yes—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—31no—
579C2×C3×C4—31no—
580C2×C3×C4—41no—
581C2×C3×C4—61no—
582C2×C3×C4—61no—
583C2×C3×C4—61no—
584C2×C3×C4—61no—
585C2×C3×C4—61no—
586C2×C3×C4—122no—
587C2×C3×C4—122no—
588C2×C3×C4—122no—
589C2×C3×C4C23×D311yescharacteristic
590C2×C3×C4C23×D311yescharacteristic
591#67—42no—
592#67—42no—
593#67—121no—
594#67—121no—
595#67—122no—
596#67—122no—
597#67—241no—
598#67—241no—
599#67—241no—
600#67—241no—
601#67—241no—
602#67—241no—
603#67—241no—
604#67—241no—
605C2×Dic3—21no—
606C2×Dic3—31no—
607C2×Dic3—31no—
608C2×Dic3—31no—
609C2×Dic3—31no—
610C2×Dic3—42no—
611C2×Dic3—61no—
612C2×Dic3—61no—
613C2×Dic3—61no—
614C2×Dic3—61no—
615C2×Dic3—61no—
616C2×Dic3—61no—
617C2×Dic3—121no—
618C2×Dic3—121no—
619C2×Dic3—241no—
620C2×Dic3—241no—
621C2×Dic3—242no—
622C2×Dic3D3×D411yescharacteristic
623C2×Dic3D3×D411yescharacteristic
624D12—21no—
625D12—21no—
626D12—21no—
627D12—21no—
628D12—21no—
629D12—21no—
630D12—42no—
631D12—42no—
632C4×D3—21no—
633C4×D3—21no—
634C4×D3—21no—
635C4×D3—21no—
636C4×D3—42no—
637C4×D3—42no—
638Dic6—21no—
639Dic6—21no—
640C3×C8—22no—
641C3×C8—61no—
642C3×C8—61no—
643C3×C8C2×#6712yes—
644C3×C8C2×#6712yes—
645C3⋊C8—21no—
646C3⋊C8—21no—
647C3⋊C8—61no—
648C3⋊C8—61no—
649C3⋊C8—121no—
650C2×C32—42no—
651C2×C32D4211yescharacteristic
652C2×C32#57511yescharacteristic
653C2×C32#57611yescharacteristic
654C3×D3—41no—
655C3×D3—41no—
656C3×D3—81no—
657C3×D3—81no—
658C3×D3—81no—
659C24—61no—
660#41—62no—
661#41—62no—
662#41—62no—
663#41—121no—
664#41—121no—
665#41—121no—
666C2×Q8—31no—
667C2×Q8C2×D3211yescharacteristic
668C2×D4—31no—
669C2×D4—31no—
670C2×D4—31no—
671C2×D4—61no—
672C2×D4—61no—
673C2×D4—61no—
674C2×D4—62no—
675C2×D4—61no—
676C2×D4—91no—
677C2×D4—121no—
678C2×D4—181no—
679C2×D4—181no—
680C2×D4—181no—
681C2×D4—181no—
682C2×D4—181no—
683C2×D4C2×D3211yescharacteristic
684C22×C4—31no—
685C22×C4—31no—
686C22×C4—61no—
687C22×C4—61no—
688C22×C4—61no—
689C22×C4—181no—
690Q16—62no—
691SD16—62no—
692SD16—62no—
693SD16—361no—
694SD16#62514yescomplemented
695D8—62no—
696D8—62no—
697D8—62no—
698D8—361no—
699M16—62no—
700C2×C8—31no—
701C2×C8—31no—
702C2×C8—62no—
703C2×C8—91no—
704C2×C8C2×D3211yescharacteristic
705C4⋊C4—91no—
706C4⋊C4—91no—
707C4⋊C4—91no—
708C4⋊C4—181no—
709C4⋊C4—181no—
710C22⋊C4—91no—
711C22⋊C4—91no—
712C22⋊C4—181no—
713C22⋊C4—181no—
714C22⋊C4—181no—
715C22⋊C4—181no—
716C22⋊C4—181no—
717C22⋊C4—181no—
718C22⋊C4—181no—
719C42—91no—
720C42—181no—
721C22×C3—22no—
722C22×C3—22no—
723C22×C3—21no—
724C22×C3—42no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3—41no—
728C22×C3—41no—
729C22×C3—61no—
730C22×C3—61no—
731C22×C3—61no—
732C22×C3—61no—
733C22×C3—61no—
734C22×C3—61no—
735C22×C3—81no—
736C22×C3—81no—
737C22×C3—121no—
738C22×C3—121no—
739C22×C3—121no—
740C22×C3—121no—
741C22×C3—121no—
742C22×C3—121no—
743C22×C3—121no—
744C22×C3—121no—
745C22×C3—121no—
746C22×C3—244no—
747C22×C3C2×D3×D411yescharacteristic
748C22×C3C2×D3×D411yescharacteristic
749C2×D3—21no—
750C2×D3—21no—
751C2×D3—21no—
752C2×D3—21no—
753C2×D3—21no—
754C2×D3—21no—
755C2×D3—41no—
756C2×D3—41no—
757C2×D3—41no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—41no—
761C2×D3—41no—
762C2×D3—41no—
763C2×D3—41no—
764C2×D3—84no—
765C3×C4—22no—
766C3×C4—22no—
767C3×C4—21no—
768C3×C4—21no—
769C3×C4—42no—
770C3×C4—61no—
771C3×C4—61no—
772C3×C4—121no—
773C3×C4#100411yescharacteristic
774C3×C4#100411yescharacteristic
775C3×C4C22×#6711yescharacteristic
776C3×C4C22×#6711yescharacteristic
777Dic3—21no—
778Dic3—21no—
779Dic3—41no—
780Dic3—61no—
781Dic3—61no—
782Dic3—61no—
783Dic3—61no—
784Dic3—121no—
785Dic3—121no—
786Dic3—121no—
787Dic3—121no—
788Dic3—121no—
789Dic3—121no—
790Dic3—241no—
791Dic3—241no—
792C32#326811yescharacteristic, complemented, Sylow
793C23—21no—
794C23—31no—
795C23—31no—
796C23—61no—
797C23—61no—
798C23—61no—
799C23—122no—
800C23—122no—
801C23—241no—
802Q8—21no—
803Q8—61no—
804Q8—61no—
805Q8C2×#62512yes—
806D4—21no—
807D4—61no—
808D4—61no—
809D4—61no—
810D4—61no—
811D4—61no—
812D4—61no—
813D4—122no—
814D4—122no—
815D4—122no—
816D4—122no—
817D4—361no—
818D4—362no—
819D4—721no—
820D4—721no—
821D4—721no—
822D4—721no—
823D4C2×#62512yes—
824C2×C4—21no—
825C2×C4—31no—
826C2×C4—31no—
827C2×C4—61no—
828C2×C4—61no—
829C2×C4—61no—
830C2×C4—61no—
831C2×C4—61no—
832C2×C4—91no—
833C2×C4—91no—
834C2×C4—122no—
835C2×C4—122no—
836C2×C4—122no—
837C2×C4—181no—
838C2×C4—181no—
839C2×C4—721no—
840C2×C4C22×D3211yescharacteristic
841C8—61no—
842C8—61no—
843C8—181no—
844C8C2×#62512yes—
845C2×C3—21no—
846C2×C3—21no—
847C2×C3—21no—
848C2×C3—42no—
849C2×C3—42no—
850C2×C3—82no—
851C2×C3—121no—
852C2×C3—121no—
853C2×C3—241no—
854C2×C3—241no—
855C2×C3—241no—
856C2×C3#576811yescharacteristic
857C2×C3#576911yescharacteristic
858C2×C3#577311yescharacteristic
859C2×C3#577411yescharacteristic
860C2×C3D4×#6711yescharacteristic
861C2×C3D4×#6711yescharacteristic
862D3—41no—
863D3—41no—
864D3—81no—
865D3—81no—
866D3—81no—
867C22—22no—
868C22—41no—
869C22—41no—
870C22—61no—
871C22—61no—
872C22—61no—
873C22—61no—
874C22—61no—
875C22—61no—
876C22—121no—
877C22—121no—
878C22—121no—
879C22—121no—
880C22—121no—
881C22—121no—
882C22—121no—
883C22—121no—
884C22—121no—
885C22—244no—
886C22D32×D411yescharacteristic
887C4—22no—
888C4—61no—
889C4—61no—
890C4—121no—
891C4—181no—
892C4—181no—
893C4—361no—
894C4—361no—
895C4#6431311yescharacteristic
896C4C22×#62511yescharacteristic
897C3—21no—
898C3#8392211yescharacteristic, complemented
899C3#8395511yescharacteristic, complemented
900C2—42no—
901C2—121no—
902C2—121no—
903C2—241no—
904C2—241no—
905C2—241no—
906C2#1059474511yescharacteristic
907C2#1059475511yescharacteristic
908C2D4×#62511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
hypercenterC2×SD16D32
hypocenterC32#3268
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C3×#916C2semidirect
2. C2×C3×#914C2semidirect
3. #10595412C2semidirect
4. #10595244C2semidirect
5. #10592863C2semidirect
6. #10591612C2semidirect
7. #10591597C2semidirect
8. #10591586C2semidirect
9. #10591486C2semidirect
10. #10591450C2semidirect
11. #10591447C2semidirect
12. #10590887C2semidirect
13. #10590833C2semidirect
14. #10590831C2semidirect
15. #10590722C2semidirect
19. C2×C3×#239C22semidirect
23. Q8×C3⋊Dic3C22semidirect
25. C2×C3×#216C22semidirect
32. C2×C3×#204C22semidirect
34. C2×C3×D3×C8C22semidirect
40. #63914C22semidirect
45. #63908C22semidirect
50. C2×#3715C22semidirect
52. #63662C22semidirect
54. #63645C22semidirect
55. #63642C22semidirect
56. #63572C22semidirect
57. #63566C22semidirect
59. #63563C22semidirect
60. #63563C22semidirect
62. (C2×D3)⋊(C3⋊C8)C22semidirect
69. C2×#916D3semidirect
70. C2×#914D3semidirect
125. C32×SD16D4semidirect
162. C2×#239C2×D3semidirect
185. C2×#216C2×D3semidirect
225. C2×#204C2×D3semidirect
227. C2×D3×C8C2×D3semidirect
390. C3×SD16#67semidirect
391. C3×SD16#67semidirect
694. SD16#625semidirect
792. C32#3268semidirect
898. C3#83922semidirect
899. C3#83955semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C3×#9162
C2×C3×#9142
#105954122
#105952442
#105928632
#105916122
#105915972
#105915862
#105914862
#105914502
#105914472
#105908872
#105908332
#105908312
#105907222
#839553
#839223